Question

In the figure below, DG is parallel to EF and ZFDG = D

OD. 75°
G
Note: picture not drawn to scale
If m/FDG = 66° and m/EDG = 100°, what is m/FED?
OA. 100°
OB. 90°
OC. 80°

Answer 1

m∠FED = 80°

Explanation:

• We have m∠FDG = m∠DFE = 66°

• m∠EDG = 100°

• Since ∠EDG is formed from the two angles ∠FDG and ∠FDE
  m∠FDG + m∠FDE = m∠EDG

• WIth the information given this works out to:
  66 + m∠FDE =100

• m∠FDE = 100 - 66 = 34

• In triangle DEF we have three angles whose sum must be 180°
  m∠FDE + m∠DFE + m∠FED = 180
  

• Plugging in known values for m∠FDE and m∠DFE:
  34 + 66 + m∠FED = 180
  100 + m∠FED = 180
  m∠FED = 180 - 100
  m∠FED = 80°